Intrinsic pseudo-volume forms for logarithmic pairs - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Bulletin de la société mathématique de France Année : 2010

Intrinsic pseudo-volume forms for logarithmic pairs

Résumé

We study an adaptation to the logarithmic case of the Kobayashi-Eisenman pseudo-volume form, or rather an adaptation of its variant defined by Claire Voisin, for which she replaces holomorphic maps by holomorphic K-correspondences. We define an intrinsic logarithmic pseudo-volume form \Phi_{X,D} for every pair (X,D) consisting of a complex manifold X and a normal crossing Weil divisor, the positive part of which is reduced. We then prove that \Phi_{X,D} is generically non-degenerate when X is projective and K_X+D is ample. This result is analogous to the classical Kobayashi-Ochiai theorem. We also show the vanishing of \Phi_{X,D} for a large class of log-K-trivial pairs, which is an important step in the direction of the Kobayashi conjecture about infinitesimal measure hyperbolicity in the logarithmic case.

Dates et versions

hal-00358751 , version 1 (04-02-2009)

Identifiants

Citer

Thomas Dedieu. Intrinsic pseudo-volume forms for logarithmic pairs. Bulletin de la société mathématique de France, 2010, 138 (4), pp.543--582. ⟨10.24033/bsmf.2596⟩. ⟨hal-00358751⟩
37 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More